Thévenin's Equivalent Circuit

My teacher did the norton's equivalent in the class, and now for studying purposes i was trying to get to the Thévenin's one. However it seems my equations are somehow wrong, and i can't figure out why.

The Eq resistance is 8||2, which is 1.6 ohms.

I tried to apply Nodal analysis first

so,
for node V1: [tex]\frac{20-V_1}{3}=\frac{V_1-V_3}{2}[/tex]
for node V2: [tex]\frac{V_1-V_3}{2}=6+\frac{V_2-0}{5}=[/tex]
The relationship between two voltages is also known, which is [tex]V_2=V_3+10[/tex]

which gives V1=2 ; V2=0 ; V3=-10.

V1-V2 should indeed be 2, because from my teachers resolution, Vab = 2V. I don't get is how can V2 be 0? Then there can't be another voltage drop when it reaches the ground (0V)

Attached Files:

Thanks :) it means the current source is just discharging current. Like i had a current source between two earth connections.

Another question:

In nodal analysis, when calculating a current entering / leaving a node we do [tex]\frac{V_x-V_y}{R}[/tex] where [tex]V_x > V_y[/tex] My question is: what if we don't know which of the two nodes has higher voltage when writting the equations? Or should it always be possible to know ?

In nodal analysis, when calculating a current entering / leaving a node we do [tex]\frac{V_x-V_y}{R}[/tex] where [tex]V_x > V_y[/tex] My question is: what if we don't know which of the two nodes has higher voltage when writting the equations? Or should it always be possible to know ?

You don't need to know which of the two nodes has higher voltage.
All you need to do is assume that one of a voltage nodes has a higher voltage than the other node. And you can treat all nodes individually and assume that the node your currently examining has higher voltage.

For example for this circuit

We can assume Vin > Va > Vout

And we can write nodal equation

[tex]\frac{(Vin-Va)}{R1}=\frac{Va}{R3}+\frac{(Va-Vout)}{R2}[/tex]

[tex]\frac{(Va-Vout)}{R2}=\frac{Vout}{R4}[/tex]

Or we can assume when we examining Va node that Va has the highest voltage.
And this means that all current flow-out (leave) from the Va node.